On parametric oscillations of pendular and rotor systems

Different kind of parametrical phenomena in vibrating systems are presented. Nonlinear properties of rotating and pendulum dynamical systems give some interesting industrial applications. The purpose of this paper is to show the possibility to generalize the models and to find a similarity of certain physical presentations and possible analysis. The effects of non-uniform rotation of unbalanced rotor, synchronization of multiples pendulums with common vibrating base, stabilization of vertical column, auto parametrical damper etc. are included in consideratio

Multi-cutter turning process stability analysis

This work displays results of a modelling-based investigation a process of multi-cutter turning process focusing on the stability of nominal steady-state case. The modelling is based on the new surface formation equations, on the equations of motion and on a rational fraction cutting law. The influence of the parameters of the system on the stability of the steady cut is analyzed

Parametric synthesis of rod spatial vibroisolation system under arbitrarily directed external disturbance

A mathematical model of flexible-rod spatial vibroisolating suspension, describing the motion of protected object, is considered. An algorithm is proposed for solving the problem of spatial displacement of the object under the action of static forces applied in an arbitrary direction. The coefficients of stiffness matrix of the suspension are determined depending on the position of static equilibrium. It is demonstrated that, depending on the requirements by varying geometrical parameters of the rods, different dynamic properties of the suspension may be obtained

On parametric oscillations of pendular and rotor systems

Different kind of parametrical phenomena in vibrating systems are presented. Nonlinear properties of rotating and pendulum dynamical systems give some interesting industrial applications. The purpose of this paper is to show the possibility to generalize the models and to find a similarity of certain physical presentations and possible analysis. The effects of non-uniform rotation of unbalanced rotor, synchronization of multiples pendulums with common vibrating base, stabilization of vertical column, auto parametrical damper etc. are included in consideratio

Dynamic stability of a flexible rod under parametric excitation

A homogeneous rod with a constant cross section, vertically mounted and cantilevered, is considered. At the unstrained state, the rod’s axis is straight. It is supposed lateral stiffness is that the rod buckles in static conditions only under gravity and its axis bends. Flexural oscillations of the rod when its base vibrates vertically are investigated. Stabilization circumstances of the rod axis rectilinearity depending on excitation parameters, internal and external damping, and rod flexibility are determined

Investigation of vibratory drilling model with adaptive control. Part 2: mixed control of peak-to-peak vibration displacement and cutting continuity index

Chip segmentation is important condition for deep drilling efficiency improving. Chip segmentation could be ensured by sustaining stable axial self-excited vibrations of a drill. Vibrations are excited by regenerative effect when cutting edges move along the surface formed by previous passes. The conditions required for reliable chip segmentation could be created by using of a special vibratory head with an elastic element, providing tool additional axial flexibility. To maintain stable vibro-process with amplitude sufficient for chip segmentation, it’s suggested to use the vibratory head with a special actuator for adaptive feedback control proportional to a tool vibration velocity. Two algorithms of the feedback gain adaptation are proposed in the present paper: the adaptation by peak-to-peak displacement and the mixed adaptation by peak-to-peak displacement with cutting continuity index. The investigation of effectiveness of the proposed algorithms applicable to the model, described in [9], is also presented

Nonlinear regenerative dynamics analysis of the multicutter turning process

This work presents nonlinear dynamics modeling results for an investigation of continuous cut stability in multicutter turning. The dynamics modeling of the multicutter turning process is carried out through the complete mathematical model of nonlinear dynamics. The dynamic stability of the system is estimated through the possibility of self-oscillations generation (Poincaré - Andronov - Hopf bifurcation) of the cutters with lobes of the stability diagram. This paper analyzes the relationship of the axial offset and the cutter angular position for compensation of the system parameters. As a result, the analysis of the influence of the technological system parameters on the chip thickness, their cross-sectional shape and the stability of the system is carried out

Chatter suppression in boring with tool position feedback control

Regenerative self-excited vibrations (chatter) often occur in boring operation due to low stiffness of a slender cantilever holder of a tool. These vibrations lead to significant defects of a machined surface and cutting tool damages. The new chatter suppression method is proposed in the paper. Displacement signal measured in the direction which is orthogonal to machined surface is used for generating a control action in the feed direction. Linear proportional control law is applied. Mathematical model of boring process dynamics with control has been developed for validation of the proposed method efficiency and searching better values of feedback gain

Dynamic stability of a flexible rod under parametric excitation

A homogeneous rod with a constant cross section, vertically mounted and cantilevered, is considered. At the unstrained state, the rod’s axis is straight. It is supposed lateral stiffness is that the rod buckles in static conditions only under gravity and its axis bends. Flexural oscillations of the rod when its base vibrates vertically are investigated. Stabilization circumstances of the rod axis rectilinearity depending on excitation parameters, internal and external damping, and rod flexibility are determined